Data-Driven Active Learning Control for Bridge Cranes

Round 1

Reviewer 1 Report

The authors presented a control design using active learning method and real-time Koopman operator identification. The control strategy is developed to bridge cranes control problem. The paper is original and addresses a timely topic, however, it deserves some slight revision to improve its readability and completeness.

First, it is difficult to identify the reason for choosing particularly Koopman operator in a data-driven setting instead of traditional identification methods. This point should be significantly improved. In the simulation section, there is no information about the Koopman model (Which kind of the basis, dimension of the lifted model, ...). Terminal cost ''Q_f'' and reference ''x_ref'' should be written in lifted coordinates (How do we get ''z_ref''?). What is the impact of information and regularization weight in the control performance?

The following technical concerns should be addressed. When the extended state variable is defined, why ''u hat'' is defined if never more is used? In the optimization problem (Eq.(5)), the decision variable is missing. Line 115: Why ''d'' instead of ''n''. Line 150: which means ''real high-dimensional model''.

the spelling should be improved.

Line 46: fail -> fails

Line 78:  introduction -> introduced

In Section 2.2, at the end of the first paragraph ''describe->described''

Line 102: pratical ->practical

Line 118: real time->real-time

Line 119: lowercase ''We'' 

Line 124: anti-swing

In Section 3.1, first paragraph ''So as to'' and ''... collection an the quality...''

Line 130: Funcion

Next to line 134: ''generate a information''

Line 135: represent compute

Next line 138: runing

line 140: ''z_refis'' missing space

line 143: funcion

next line 147: controllers

Line 155: ''...design an active ...''

Line 164: continuous-time

Line 165: real-time

Line 166,185, Table 1 step 8,  Koopman (capital letter K).

Line 188: 0.5m missing space.

Line 191: remain

Line 203: ''are adjust as Table 3 showed''

Line 220: refer

Line 249: throug

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The trolley position control seems to be far too slow. In particular, compared to more recent results on crane control, e.g.

Data-driven modeling for damping and positioning control of gantry crane, Maksakov et al. https://doi.org/10.1016/j.ymssp.2023.110368

Can you please comment on this?
Also, you state that the benefit of your online learning approach is, that not a large amount of offline data is required. However, this won't be a problem if you use simulation data. Maybe you could comment on this, too.

no comments

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The authors propose the data-driven active learning control for bridge cranes where active learning is used to learn Koopman operator representation of the bridge crane. The LQT regulator is synhtesised. 

I have the following comments:

1) The authors claim that the actual bridge crane system is very complex nonlinear system, and the precise modeling results of the system cannot be

obtained by using mathematical theory or system identification theory. However, there are numerous experiementally validated control algorithms and nonlinear mathematical models in the literature. Therefore, a stronger motivation for the data-driven approach should be given in the introduction. This can be done by describing some possible sources of nonlinearity that is present in a real system but hard to model (for example friction, backlash, flexible-rope, dead-zones etc.). The previous comment holds true especially since a simplified nonlinear model is presented. 

2) The Koopman-operator is not used to overcome issues with data-driven modeling, instead it is used to approximate a nonlinear system with a higher dimensional but linear one. Of course it can be used for data-driven system identification, as described. 

3) Even though the paper is interesting, the main problem with the proposed method is that the recorded trajectory has to be informative enough, presistently exciting and safe. For example a large swing angle can not be allowed even during system identification on a real system.  Is it possible to limit the state variables during the learning process?

4) Please show the control input in all the plots and indicate the maximum allowed value

5) From the figures it seems to me that the CSMC controller outperforms the proposed one. System such as crane usually allows for limited swing during motion and requires a system to stop without residual oscillations.  CSMS has a faster response, and comparable maximum sway angle. 

6) It would be interesting how does the proposed algorithm performs when additional nonlinearity such as dead-zone is present. 

7) What are ILC, CSMC? The abbreviations are undefined. 

 There are some typos in the text. For example throug. In some cases the Koopman is not written with capital letter K. 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

This is the revised version of the manuscript. The authors have addressed most of my comments given in the previous round of review. My only comment is related to the dead-zone compensation. Of-course if the dead zone is perfectly compensated, there is no difference to the nominal case. I wanted you to include the results where the dead zone is not compensated but instead learned from the data by the Koopman operator. The main idea was to show the capability of the data-driven approach to learn some nonlinearity that is typically present in the crane system. 

Author Response

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Author Response File: Author Response.pdf